Paper
Concentration of the truncated variation of fractional Brownian motions of any Hurst index, their $1/H$-variations and local times
Authors
Witold M. Bednorz, Rafał M. Łochowski
Abstract
We obtain bounds for probabilities of deviations of the truncated variation functional of fractional Brownian motions (fBm) of any Hurst index from their expected values. Obtained bounds are optimal for large values of deviations up to multiplicative constants depending on the parameter only. As an application, we give tight bounds for tails of -variations of fBm along Lebesgue partitions and establish the a.s. weak convergence (in ) of normalized numbers of strip crossings by the trajectories of fBm to their local times for any Hurst parameter .